Solving 10-14 Equivalence Arguments: R to neg(w v s)

In summary, the conversation is discussing logical implications and negations. Starting with the first statement, "neg[r\implies neg(w v s)]", it is inferred that "r" implies "neg(w v s)". The next statement, "R", is then added to the equation, resulting in "R^(wvs)". From this, it can be concluded that "neg(w v s)" is true.The third statement, "r\implies neg(w v s)", is then repeated, followed by "w v s". This leads to the statement "neg R", indicating that "R" must be false.The final statement, "(w v s)\implies neg r", suggests that "w v s" implies
  • #1
chelseajjc95
4
0
10.) neg[r\implies neg(w v s)] 13.) r\implies neg(w v s)
----------------------------- R
R^(wvs) --------------------------
neg(w v s)
11.) r\implies neg(w v s)
w v s 14.) r\implies neg(w v s)
------------------------- -------------------------
neg R (w v s)\implies neg r

12.) R
---------------
r v (w v s)
 
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  • #2
Your post is hard to read. Please do the following to improve it.

  1. Use formula editor to typeset formulas.
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  5. Write the problem statement in the post body rather than the post title, following https://mathhelpboards.com/rules/.
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  8. Explain the missing problem 14.
 

FAQ: Solving 10-14 Equivalence Arguments: R to neg(w v s)

What is the purpose of solving 10-14 equivalence arguments?

The purpose of solving 10-14 equivalence arguments is to determine if two statements, R and neg(w v s), are logically equivalent. This means that the truth values of these statements will always be the same, regardless of the truth values of their individual components.

How do you solve 10-14 equivalence arguments?

To solve 10-14 equivalence arguments, you must use logical equivalences and rules of inference to manipulate the statements and determine if they are logically equivalent. This involves breaking down the statements into their individual components and applying logical operations to them.

What are the steps to solving 10-14 equivalence arguments?

The steps to solving 10-14 equivalence arguments are as follows:

  1. Break down the statements R and neg(w v s) into their individual components.
  2. Apply logical equivalences and rules of inference to manipulate the statements.
  3. Determine if the truth values of the statements are always the same.
  4. If the truth values are always the same, then the statements are logically equivalent.

What are some common logical equivalences used in solving 10-14 equivalence arguments?

Some common logical equivalences used in solving 10-14 equivalence arguments include De Morgan's Laws, double negation, and the distributive and associative properties. These equivalences allow you to manipulate the statements and determine if they are logically equivalent.

Why is it important to solve 10-14 equivalence arguments accurately?

It is important to solve 10-14 equivalence arguments accurately because they are commonly used in mathematics, computer science, and other fields to prove the validity of arguments and logical statements. If the equivalence is not accurately determined, it could lead to faulty reasoning and incorrect conclusions.

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